Chapter 5: Two Dimensions and Beyond

Section 4: Substitution Systems and Fractals

Dragon curve

The pattern shown here can be obtained in several related ways, including from numbers in base ⅈ-1 (see below) and from a doubled version of the paths generated by 1D paperfolding substitution systems (see page 892). Its boundary has fractal dimension 2 Log[2, Root[2 + #2 - #3, 1]] ≃ 1.52.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]